Sherwood 2015

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approvedabstract-1.pdf2015-01-15 07:51:47Di Hu

Revealing the meaning of the asymptotic matching across the resistive resonant layer in MHD

Author: Di Hu
Requested Type: Poster Only
Submitted: 2015-01-14 09:41:26

Co-authors: Leonid E Zakharov

Contact Info:
Peking University
209, Chengfu Road
Beijing, Beijing   100871

Abstract Text:
In the high temperature plasma of tokamaks the macroscopic magnetic perturbations preserve poloidal and toroidal magnetic fluxes both frozen into the plasma. Only at the plasma edge (or plasma-vacuum interface) and at the resonant surfaces the highly localized currents are excited, which cause local violation of the flux frozenness into the plasma. At the resonant surface the resistive diffusion leads to formation of magnetic islands.

In this presentation we consider the situation, which marginally unstable to the resistive MHD modes. In the absence of pressure gradient it is well described by the asymptotic Delta-prime theory of the tearing modes. In this case 2 MHD solutions outside the resistive layer behave
like u_1(x)=x and u_0(x)=1+au_1*ln|x|+b*x, where x is the distance from the resonant surface. The match coefficient are determined by boundary conditions.

The matching technique uses only ideal solutions to judge the resistive instabilities. In particular, the most essential information about the threshold is determined by condition that u_0,u_1 match each other from both sides at xto0.

In the presence of p' the behavior is different: u_0to|x|^{-nu}, u_1to x |x|^nu, and u_1/u_xto x|x|^{2*nu} with nu proportional to p' and inverse proportional to local shear. The question is what would be the meaning of matching both solutions when nu>1. In this case, the disconnection of the small solutions does not even perturb the value of the second derivative in the total solution, so even the current density remains unperturbed.

This question has a practical importance for spherical tokamaks where the low shear in the core corresponds to the discharges with the highest achievable beta. When the high-beta plasma approaches the ideal stability limit, it should face first the resistive stability limit. But in this case the nu exponent can exceed 1, and it is necessary to understand what would be meaning, if any, of the matching technique.


March 16-18, 2015
The Courant Institute, New York University